"No evidence of other injured people and more perpetrators was found," Xinhua news agency quoted the police as saying.
"We have currently no evidence of a terrorist background indeed," he said, asking public not to spread rumours.
The gunman was a patient of the doctor in that clinic.
Germany is shocked by the violent attacks that happened last week in the southern part of the country.
On Sunday, a 22-year-old Syrian refugee armed with a machete killed a pregnant woman in the city of Reutlingen, and injured two others.
The same evening, a 27-year-old Syrian blew himself up and wounded at least 15 persons outside a music festival in Ansbach, a city in southern German state of Bavaria.
On July 22, an 18-year-old German-Iranian man holding dual citizenship fatally shot nine persons in a Munich shopping mall, and injured 35.
Earlier, on July 18, a 17-year-old Afghan attacked passengers with an axe aboard a train near Wurzburg, injuring four before being shot by security men.
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